Dynamic adaptive video streaming over HTTP (DASH) plays a crucial role in delivering video across networks. Traditional adaptive bitrate (ABR) algorithms adjust video segment quality based on network conditions and buffer occupancy. However, these algorithms rely on fixed rules, making it challenging to achieve optimal decisions considering the overall context. In this paper, we propose a novel deep-reinforcement-learning-based approach for DASH streaming, with the primary focus of maintaining consistent perceived video quality throughout the streaming session to enhance user experience. Our approach optimizes quality of experience (QoE) by dynamically controlling the quality distance factor between consecutive video segments. We evaluate our approach through a comprehensive simulation model encompassing diverse wireless network environments and various video sequences. We also conduct a comparative analysis with state-of-the-art methods. The experimental results demonstrate significant improvements in QoE, ensuring users enjoy stable, high-quality video streaming sessions.